A sleeve valve is a type of valve usable in internal combustion engines, including but not limited to opposed piston engines, in which two pistons share a single cylinder, and also in engines in which each piston reciprocates in its own cylinder. Such a valve typically forms all or a portion of the cylinder wall. In some variations, one or more sleeve valve can reciprocate back and forth substantially in parallel to an axis upon which one or more pistons reciprocates to open and close intake and/or exhaust ports at appropriate times to introduce air or an air-fuel mixture into the combustion chamber and/or to exhaust combustion products from the chamber. In other variations, one or more sleeve valve can rotate about and/or translate along the axis of the piston or pistons to open and close one or both of the intake and exhaust ports. Due to the potentially large circumferential port area that can be controlled by a sleeve valve, such valves can provide a relatively large cross sectional area for fluid flow in the open position.